Calculator Form
Use the near-surface model. Enter three known values. Leave the unknown value blank. Its unit still controls the displayed result.
Example Data Table
| Mass (kg) | Gravity (m/s²) | Height (m) | Potential Energy (J) |
|---|---|---|---|
| 2.0 | 9.81 | 5.0 | 98.10 |
| 5.0 | 9.81 | 12.0 | 588.60 |
| 10.0 | 3.71 | 20.0 | 742.00 |
| 25.0 | 1.62 | 8.0 | 324.00 |
| 50.0 | 9.81 | 15.0 | 7357.50 |
Formula Used
The calculator uses the near-surface gravitational potential energy equation:
E = m × g × h
E is potential energy in joules. m is mass in kilograms. g is gravitational field strength in meters per second squared. h is vertical height in meters.
Rearranged forms are also used:
- m = E ÷ (g × h)
- g = E ÷ (m × h)
- h = E ÷ (m × g)
This model works well for everyday height changes near a planet surface. It does not model large orbital distance changes.
How to Use This Calculator
- Choose the variable you want to solve for.
- Pick mass, height, and energy units that fit your problem.
- Select a gravity preset or type a custom gravity value.
- Enter the three known values.
- Leave the unknown field blank.
- Choose the decimal precision you want.
- Press Calculate Now.
- Review the result, chart, and downloadable summary.
About This Physics Calculator
What the calculator does
This calculator helps you work with gravitational potential energy in a direct way. It uses the familiar near-surface equation. That equation connects mass, gravity, and height. When you know three values, you can solve the fourth one quickly.
Why unit flexibility matters
Physics problems often come from mixed sources. A worksheet may use kilograms. A field note may use pounds or feet. This page converts those values before solving. That reduces manual conversion errors. It also lets you display the answer in the unit you prefer.
How the result is interpreted
Gravitational potential energy measures stored energy due to position. A larger mass creates more potential energy. A greater height also increases it. Stronger gravity increases it too. The relationship is linear. If one variable doubles, energy doubles when the others stay fixed.
When to use the near-surface equation
The equation on this page is best for everyday vertical motion close to a planet surface. It works for lifting boxes, lab masses, climbing systems, and classroom examples. It is also useful for engineering estimates. For large orbital changes, a universal gravitation model is more suitable.
Why the graph helps
The Plotly graph shows how energy changes as height changes. This gives a clear visual pattern. Students can see proportional growth. Teachers can use the chart in demonstrations. Analysts can also use the export buttons to save a clean summary for reports, notes, or reviews.
Frequently Asked Questions
1. What does gravitational potential energy mean?
It is stored energy due to an object's position in a gravitational field. Near a surface, it depends on mass, gravity, and vertical height.
2. Which equation does this page use?
It uses the near-surface equation E = m × g × h. This is the standard classroom and practical form for small vertical height changes.
3. Can I solve for mass instead of energy?
Yes. Choose Mass in the solve menu, enter energy, gravity, and height, then submit the form to calculate the missing mass value.
4. Why are gravity presets included?
They help you test the same object on different worlds quickly. A preset fills the gravity field so you can compare results faster.
5. Does this calculator support feet and pounds?
Yes. It supports several common mass and height units. The page converts them internally before applying the equation.
6. When should I avoid this equation?
Do not use it for large orbital distance changes. In that case, gravitational potential energy varies with radius and needs a different model.
7. What does the graph show?
It shows potential energy versus height using the current mass and gravity values. That makes the linear relationship easier to inspect.
8. What do the export buttons save?
The CSV button saves a compact result table. The PDF button creates a simple report summary with the solved variable and values.